Problem: Simplify the following expression: $k = \dfrac{30b + 30a}{10a + 15} - \dfrac{30c - 10a}{10a + 15}$ You can assume $a,b,c \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{30b + 30a - (30c - 10a)}{10a + 15}$ $k = \dfrac{30b + 40a - 30c}{10a + 15}$ The numerator and denominator have a common factor of $5$, so we can simplify $k = \dfrac{6b + 8a - 6c}{2a + 3}$